1. Field of the Invention
This invention relates generally to magnetic levitation and levitated kinetic energy storage devices.
2. Related Technology
The generation and distribution of electrical energy is critical to the normal operation of vast components of our industry and culture. Electricity is typically created as needed through the combustion of carbon-based fuels, conversion of water power, fission of radioactive elements, and various other techniques. However in many instances it is desirable to store electricity for use at a later time. For example, stored electricity can improve power supply quality by providing “ride-through” for momentary outages, reducing harmonic distortions, and eliminating voltage sags and surges. Stored electricity also increases the value of renewable energies such as photovoltaic, wind and wave-generated electricity by allowing that energy to be stored and supplied later at periods of peak consumer demand. Stored electricity may be held in reserve to prevent interruptions of service by the failure of an operating generating station or transmission link. Inexpensive off-peak electricity may also be stored for use during relatively expensive on-peak hours. The ability to store electricity also enables a utility to postpone construction of additional generating capacity or installation of new transmission or distribution lines and transformers by supplementing the existing facilities with stored resources as demand growth approaches capacity.
A variety of technologies for electrical energy storage are in current use or development. The pumped hydro technique utilizes two large reservoirs at different elevations. Water is pumped to the high reservoir and stored as potential energy. Upon demand, water is released through hydraulic turbines into the low reservoir to generate up to 1000 MW. Compressed air energy storage (CAES) uses off-peak energy to compress and store air in underground caverns or large buried pipes. Upon demand, stored air is released, heated and expanded through a combustion turbine to create electrical energy. Batteries use an electrochemical reaction to store energy in a chemical form. Upon demand, reverse chemical reactions cause electricity to flow out of the battery and back to the grid. Batteries are manufactured in capacities ranging from milliwatts to modular configurations of megawatts. Superconducting magnetic energy storage (SMES) stores energy in the magnetic field created by the flow of direct current in a coil of superconducting material immersed in liquid helium and contained in a vacuum-insulated cryostat. Ultracapacitors are comprised of two oppositely charged electrodes, a separator, an electrolyte and current collectors. Charge is stored by ions as in a battery but no chemical reaction takes place. Flywheels utilize a disk spun up to high velocity by a motor/generator to store power as kinetic energy. Upon demand that energy is extracted by the generator as electrical power. The use of magnetic bearings and a vacuum chamber helps reduce energy losses.
The primary barrier to increased use of the aforementioned storage technologies is installation costs. Batteries, flywheels, SMES, and ultracapacitors all cost far too much to be used in large installations. CAES systems can be scaled up to moderately large capacity, but need a constant supply of fuel. They are similar in size and characteristics to conventional turbine power plants, i.e. large and noisy, making them impractical in many areas. They also have a cold startup time of 15 minutes, making them unusable in some applications. Pumped hydro was the premier storage system for decades, with over 22 gigawatts of capacity installed in the U.S., but geographic, geologic and environmental constraints associated with reservoir design as well as increased construction costs have made them impractical for future expansion. Thus far no technology has been discovered that is capable of cost-effectively replacing pumped hydro. Therefore the industry badly needs a fundamentally new approach to circumvent existing problems.
With the advent of high strength, lightweight materials such as carbon fiber, flywheels showed promise as primary energy storage devices. Flywheels of this kind have proven capable of providing high power and relatively high storage capacity per unit mass, but do not scale up well. FIG. 1a illustrates the basic design of a current technology flywheel. In flywheel system 8 a flywheel rim 18 is attached by spokes or hub 16 to a central shaft 10, which is supported by bearings 12. The bearings 12 may be mechanical bearings such as ball bearings or, as is generally the case in high performance flywheels, non-contact magnetic bearings. A motor-generator 14 operates as a motor to spin the flywheel up to speed to store energy, and as a generator to extract stored energy. The kinetic energy stored in the rotor (rim) is proportional to the mass of the rotor and the square of its velocity. The stored kinetic energy, K.E., is:K.E.=½Jω2=½kmr2ω2  (1)where ω is the rate of rotation in radians per second, J is the moment of inertia about the axis of rotation in kilogram-meters squared, m is rotor mass, r is the effective rotor radius (also known as the radius of gyration), and k is an inertial constant dependent on rotor shape. For a solid disk of uniform thickness, k=½. If the rotor is a thin ring, k=1. In other words, a spinning ring contains twice as much kinetic energy per unit mass as a spinning cylinder.
The stress produced in the rim is proportional to the square of the linear velocity at the tip or outside diameter of the rim. When rim speed is limited by the tensile strength of the rim material, the maximum linear tip velocity is constant, regardless of radius. The maximum rotation rate is then inversely proportional to rim diameter. For example, if a particular material allows a rotor tip speed of 1000 meters per second, a 0.5 meter diameter rim would have a maximum spin rate of 39,000 RPM, whereas a 2-meter rim constructed of the same material would have a maximum spin rate of 9550 RPM.
For maximum stored energy the rim must be spun at the highest possible speed. Therefore the best materials for rim construction are not the densest or the strongest, but rather they are those with the highest specific strength, i.e. the ratio of ultimate tensile strength to density. For a thin rim, the relationship between maximum rim stress and specific energy or energy stored per unit mass of rim is:K.E./m=σh/2ρ  (2)where σh is the maximum hoop stress the rim can withstand in N/rn2 and ρ is the density of the rim material in kg/m3. In other words, specific energy corresponds directly to the specific strength σh/ρ of the material from which the rim is formed. Accordingly, filament-wound rims made of high strength, low density fibers store more energy per unit weight than metal rims. Carbon fiber rims have attained tip speeds in excess of 1000 meters per second. These rims are typically housed in evacuated chambers to minimize energy losses due to air drag and to eliminate aerodynamic heating.
As rotational velocity increases, the centrifugal force on the rim 18 is greater than the centrifugal force on the shaft 10 and so the rim 18 expands faster than shaft 10. The spoke assembly 16 must compensate for this differential in rate of growth while maintaining a secure bond with the rim. The resulting stress concentrations are illustrated in FIG. 1b. High-speed carbon composite rims can expand by more than 1% in normal operation. Other materials, such as E-glass, can expand even more. This relative growth makes hub design one of the limiting factors in flywheel diameter. One common failure mode resulting from this differential growth is separation of the rim from the hub caused by hoop stress, which is highest at the inner boundary of the flywheel and decreases rapidly from the inner boundary of the rim to the outer boundary. Another common failure mode is delamination of the layers of fibers that make up the rim. These fibers are extremely strong along their length but are held together in the radial direction only by relatively weak epoxy binder. The thicker the rim is in the radial direction, the higher the delaminating forces become.
Many methods have been proposed to alleviate this problem, usually involving exotic materials or complicated flywheel structures. However, these techniques are very expensive and are only useful for flywheels of rather modest size, usually well under a meter in diameter. One technique involves the use of multiple filament-wound rims separated by elastomeric interlayers to prevent the radial transmission of tensile stresses between the various rims. To obtain the highest speed and minimize costs, high strength carbon fiber is used in the outermost rims, while lower strength (and cost) carbon fiber or glass is used for the inner rims. Other techniques include varying the density of the rim as a function of radius by means of ballasting, e.g. with lead particles, and using a combination of layers of fibers each having a different modulus of elasticity. Another technique, depicted in FIGS. 2a and 2b, is described in U.S. Pat. No. 6,211,589. Instead of multiple concentric rims, this rotor 32 is a simple thin-rimmed wheel, greatly decreasing the differential stress problem in a much less complex way. A relatively thin rim is less subject to differential stress and capable of higher rotation rates. As described previously, this also results in higher energy content per unit mass of rotor material. The rotor is supported by spoke assembly 34 and magnetic bearing assembly 36, and spins around shaft 38. The spokes are constructed such that they stretch as the flywheel spins up, in theory allowing them to compensate for expansion of the wheel and thereby eliminating the separation problem. However in actual operation this structure has proven to be unstable.
A different technique is to eliminate the hub and spoke assemblies entirely to create a simple spinning ring. With no hub assembly the failure mode in which the rim separates from the hub no longer pertains. FIG. 3 shows a cross section of a ring system using permanent magnet bearings as disclosed by Lee, Kwan-Chul; Chung, Kie-Hyung; Kim; Dong-II; Cho, Chang-Ho, “Conceptual design of a hoop energy storage system,” Journal of Applied Physics, Vol. 81, No. 8, April 1997. This system 40 utilizes a spinning composite ring 42 having permanent magnets 44 and 46 provided underneath the ring 42 for levitation. Permanent magnets 48 and 50 located along the inside diameter provide stabilization. A motor/generator 52 injects and extracts energy.
While the use of permanent magnet bearings has the potential for low induced currents and drag, the aforementioned magnet configuration has fundamental problems. Simple opposed magnets provide relatively low levitation force per unit area, resulting in limited spinning mass and low energy storage capacity or a high cost for magnets. Further, simple opposed stabilization magnets do not provide stability due to the constraints of Earnshaw's theorem. Without additional restraint or control the ring will immediately slide into contact with the support structure. Ring expansion due to rotation-induced stress widens the gap between the stationary and spinning stabilization magnets as speed increases, further weakening their affect. Further, the permanent magnets attached to the underside of the ring will be subject to intense lateral forces due to high speed ring rotation. Permanent magnets such as neodymium-iron-boron provide high field strength, but have low tensile strength. If not carefully supported, these magnets can easily be shattered by lateral forces causing the ring to crash and self-destruct. In addition, the thick structure of the ring also results in differential stress and expansion problems as encountered in conventional flywheel designs. Thus the rotation rate of the ring must be severely limited or it will delaminate.
The idea of a hubless flywheel continues to have merit, but for such a design to succeed it must offer a number of features, including stable levitation with low eddy current drag, efficient use of permanent magnets to keep costs low, a method to prevent ring expansion from disabling the stabilization and/or levitation, a method to prevent ring expansion from delaminating and destroying the ring itself, and a method to mount and support permanent magnets on the ring such that intense lateral forces will not shatter them. These features are not offered by the current technology.